Problem: Let N be a positive even number.

We have a permutation of (1, 2, ..., N), p = (p_1, p_2, ..., p_N). Snuke is constructing another permutation of (1, 2, ..., N), q, following the procedure below.

First, let q be an empty sequence. Then, perform the following operation until p becomes empty:

* Select two adjacent elements in p, and call them x and y in order. Remove x and y from p (reducing the length of p by 2), and insert x and y, preserving the original order, at the beginning of q.



When p becomes empty, q will be a permutation of (1, 2, ..., N).

Find the lexicographically smallest permutation that can be obtained as q.

Constraints

* N is an even number.
* 2 ≤ N ≤ 2 × 10^5
* p is a permutation of (1, 2, ..., N).

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the lexicographically smallest permutation, with spaces in between.

Examples

Input

4
3 2 4 1


Output

3 1 2 4


Input

2
1 2


Output

1 2


Input

8
4 6 3 2 8 5 7 1


Output

3 1 2 7 4 6 8 5

Solution (in PYTHON3):

Solution:
def main():
    n = int(input())
    p = list(map(lambda x: int(x)-1, input().split()))

    pos = [j for i, j in sorted([(j, i) for i, j in enumerate(p)])]
    basesize = n >> 1
    num = 1
    while num < basesize:
        num *= 2
    num -= 1

    tree_even = [100001]*(num*2+1)
    tree_odd = [100001]*(num*2+1)

    for i in range(num, num+basesize):
        tree_even[i] = p[(i-num)*2]
    for i in range(num-1, -1, -1):
        tree_even[i] = min(tree_even[2*i+1:2*i+3])
    for i in range(num, num+basesize):
        tree_odd[i] = p[(i-num)*2+1]
    for i in range(num-1, -1, -1):
        tree_odd[i] = min(tree_odd[2*i+1:2*i+3])

    g = dict()
    d = dict()
    q = [n-1]
    qap, qp = q.append, q.pop
    while q:
        t = qp()
        m, M = t//n, t % n
        if m+1 == M:
            d[t] = p[m]*n+p[M]
            continue
        g[t] = []
        gap = g[t].append
        if m % 2 == 0:
            i1, j1 = m >> 1, (M >> 1)+1
            even = 200000
            l, r = i1+num, j1+num
            while l < r:
                if r % 2 == 0:
                    r -= 1
                    even = min(even, tree_even[r])
                if l % 2 == 0:
                    even = min(even, tree_even[l])
                    l += 1
                l >>= 1
                r >>= 1
            even_idx = pos[even]
            odd = 200000
            l, r = (even_idx >> 1)+num, j1+num
            while l < r:
                if r % 2 == 0:
                    r -= 1
                    odd = min(odd, tree_odd[r])
                if l % 2 == 0:
                    odd = min(odd, tree_odd[l])
                    l += 1
                l >>= 1
                r >>= 1
            odd_idx = pos[odd]
            d[t] = even*n+odd
            if m != even_idx:
                s = m*n+even_idx-1
                qap(s)
                gap(s)
            if M != odd_idx:
                s = (odd_idx+1)*n+M
                qap(s)
                gap(s)
            if even_idx+1 != odd_idx:
                s = (even_idx+1)*n+odd_idx-1
                qap(s)
                gap(s)
        else:
            i1, j1 = m >> 1, M >> 1
            odd = 200000
            l, r = i1+num, j1+num
            while l < r:
                if r % 2 == 0:
                    r -= 1
                    odd = min(odd, tree_odd[r])
                if l % 2 == 0:
                    odd = min(odd, tree_odd[l])
                    l += 1
                l >>= 1
                r >>= 1
            odd_idx = pos[odd]
            even = 200000
            l, r = (odd_idx >> 1)+1+num, j1+1+num
            while l < r:
                if r % 2 == 0:
                    r -= 1
                    even = min(even, tree_even[r])
                if l % 2 == 0:
                    even = min(even, tree_even[l])
                    l += 1
                l >>= 1
                r >>= 1
            even_idx = pos[even]
            d[t] = odd*n+even
            if m != odd_idx:
                s = m*n+odd_idx-1
                qap(s)
                gap(s)
            if M != even_idx:
                s = (even_idx+1)*n+M
                qap(s)
                gap(s)
            if odd_idx+1 != even_idx:
                s = (odd_idx+1)*n+even_idx-1
                qap(s)
                gap(s)

    g2 = dict()

    for i, t in g.items():
        k = d[i]
        g2[k] = []
        ga = g2[k].append
        for j in t:
            ga(d[j])

    import heapq
    h = [d[n-1]]
    heapq.heapify(h)
    ans = []
    hpop = heapq.heappop
    hpush = heapq.heappush

    while h:
        t = hpop(h)
        ans += [t//n+1, t % n+1]
        if t in g2:
            for s in g2[t]:
                hpush(h, s)

    print(*ans)


main()